Initial-boundary value problem for second order hyperbolic operator with mixed boundary condition

We deal with a linear hyperbolic differential operator of the second order on a bounded planar domain with a smooth boundary. We establish a well-posedness result in case where a mixed, Dirichlet-Neumann, boundary condition is prescribed on the boundary. We focus on the case of a nonhomogeneous Dirichlet data and a homogeneous Neumann one